Jurgen Klopp’s side head to the Italian capital on Wednesday with a 5-2 advantage from the first leg and do so the back of a Premier League match they controlled for long periods without over-exerting themselves in search of a winner.
The result left Liverpool with a healthy cushion over fifth-placed Chelsea and in need of a maximum of four points from their two remaining matches to guarantee qualification for Champions League.
Relegation-threatened Stoke remain in the drop zone with only two games left to avoid slipping into the Championship.
Klopp’s programme notes featured a message he has stated with regularity in recent weeks; that Liverpool’s focus on a top four finish in the Premier League should not be neglected despite their progress in European competition.
The Reds manager made five changes from the side which beat Roma, with Sadio Mane the most notable absentee from the starting line-up with a thigh problem.
However, despite Klopp’s words, it was almost inevitable the intensity of that thrilling victory over the Italian side would not be replicated against Stoke.
The Potters have never won a top-flight match at Anfield – the longest winless away run in top-flight history – with their last league victory in Division Two in 1959.
There was never any danger of that statistic being altered as Liverpool dominated, yet only sporadically tested visiting goalkeeper Jack Butland.
This was also a game where Mohamed Salah endured, by his exceptionally high standards, a rare off day.
Indeed it was the first time since Liverpool’s match against Swansea on December 26 last year that Salah has not found the net in the Premier League on home turf.
The Egypt international did have a golden opportunity to score his 32nd league goal of the season in the fifth minute.
Salah was sent clear and when he clipped the ball over Jack Butland the Liverpool supporters were celebrating, only for disbelief to dawn when the shot did not hit the target.
Stoke’s attacking ambition was fleeting and largely centred around seeking to hit Liverpool on the counter attack.
A tame header from Mame Diouf, which hit the side netting, was the best the visitors could muster in a first half in which Liverpool monopolised the clear-cut opportunities.
Trent Alexander-Arnold, who started in midfield, got the ball stuck under his feet after he had exchanged passes with Salah but was unable to generate sufficient power to trouble Butland.
Georginio Wijnaldum hit the side netting from distance, Salah curled a free-kick just wide, while Danny Ings volleyed in from a tight angle only for the assistant referee to flag him offside.
There was a hush around Anfield just before half-time when captain Jordan Henderson lay on the turf clutching his Achilles, however after treatment the midfielder was able to continue.
Attacking the Kop End in the second half, Liverpool’s tempo increased although it failed to translate into clear goalscoring chances.
Liverpool’s players vociferously appealed for a penalty three minutes from time when the ball struck the arm of Erik Pieters inside the box from Wijnaldum’s cross but referee Andre Marriner waved them away.
Stoke then went close at the death when Diouf’s low cross flashed across the area with nobody able to apply the decisive touch, but Paul Lambert will have been more than satisfied with a point.